Let (X) be an arbitrary set and (mathscr{F} subset mathscr{P}(X)). Show that [sigma(mathscr{F})=bigcup{sigma(mathscr{C}): mathscr{C} subset mathscr{F} text

Question:

Let $X$ be an arbitrary set and $\mathscr{F} \subset \mathscr{P}(X)$. Show that

\[\sigma(\mathscr{F})=\bigcup\{\sigma(\mathscr{C}): \mathscr{C} \subset \mathscr{F} \text { countable sub-family }\}\]

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Measures Integrals And Martingales

ISBN: 9781316620243

2nd Edition

Authors: René L. Schilling

See More Books

Question Posted: Jan 23, 2024 10:00 AM

See More Questions

The null hypothesis is Ho:u1 = u2 and the alternative hypothesis is as specified. The data available below are from a simple random paired sample from the two populations under consideration. Use the...
How do social norms contribute to the maintenance of social order and stability, while also serving as mechanisms for social control and the enforcement of conformity?
Imagine we have the data frame below and we have named it "df" in R. worker wage state 1 11 2 9 3 20 4 40 5 5 CA CA AZ AZ OR In the R console I type: mean(wage) But receive the error "object 'wage'...
On December 1, 2011, Lavender Manufacturing Company (a corporation) purchased another company's assets, including a patent. The patent was used in Lavender's manufacturing operations; $49,500 was...
Consider the conditions of Problem 1.18. With heat transfer by convection to air, the maximum allowable chip power is found to be 0.35 W. If consideration is also given to net heat transfer by...
Bork Corporation wishes to borrow $100,000 for one year. It has the following alternatives available to it. a. An 8 percent loan on a discount basis with 20 percent compensating balances required. b....
The mean and standard deviation of a random sample of n measurements are equal to
Nathan T Corporation is comparing two different options. Nathan T currently uses Option 1, with revenues of $65,000 per year, maintenance expenses of $5,000 per year, and operating expenses of...
Find the 40th percentile of the present value of $1 of whole-life insurance, benefit payable immediately upon death, issued to a person aged 25. Use ILT and assume UDD.
Extend Proposition 4.3 ( i ) 4.3 ( i ) , (iv) and (v) to finitely many sets A 1 , A 2 , , A N A A 1 , A 2 , , A N A . Data from proposition 4.3 Let (X, A,) be a measure space and A, B, An, BnA,...
Monotone classes (1). A family $\mathscr{M} \subset \mathscr{P}(X)$ which contains $X$ and is stable under countable unions of increasing sets and countable intersections of decreasing sets. is...
A ball is selected from a bin of balls numbered from 1 through 52. It is replaced, and then a second numbered ball is selected from the bin. Determine whether the events are independent or dependent....
1. The KYM company wants to invest $ 523,000 pesos in the bank that guarantees a simple interest rate of 3.32% quarterly. If the company is considering the 8-month investment. What amount will you...
3. (5 points) The uncertainty principle limits our ability to determine simultaneously the position and momentum of a particle. (a) Why were classical physicists unaware of the limitations that this...
CASE STUDY Patient Name Valarie Ramirez Attending Paul F. Buckwalter, MD PATIENT INFORMATION DOB 08/04/1986 Allergies MAN 00-AA-006 Penicillin Other Information Past HX: AB x1 Valarie Ramirez arrives...
Petesy Corporation is preparing its Master Budget for 2019. Budget information is as follows: SalesProduction CostOperating Expenses 20191 st Quarter P280,000P192,000P64,000 2 nd Quarter 320,000...
A steady flow of 20 m3/s of moist air at TDB = 35iC, TWB = 25iC, 100 kPa (state 1) is dehumidified by first cooling it and condensing out moisture (state 2), then reheating it to 20iC and 50% R.H....
An initial public offering (IPO) of a company's stock is considered "under-priced" if there is a large percentage difference between its issuing price and its closing price after one day of trading....
Describe basic managerial approaches to implementing controls and how these are implemented.
Let $\left(P_{t}ight)_{t \geqslant 0}$ and $\left(T_{t}ight)_{t \geqslant 0}$ be two Feller semigroups with generators $(A, \mathfrak{D}(A))$, resp. $(B, \mathfrak{D}(B))$. a) If...
Let $A, B \in \mathbb{R}^{d \times d}$ and set $P_{t}:=\exp (t A):=\sum_{j=0}^{\infty}(t A)^{j} / j$ !. a) Show that $P_{t}$ is a strongly continuous semigroup. Is it contractive? b) Show that...
Show that $\mathcal{C}_{\infty}:=\left\{u: \mathbb{R}^{d} ightarrow \mathbb{R}ight.$ : continuous and $\left.\lim _{|x| ightarrow \infty} u(x)=0ight\}$ equipped with the uniform topology is a...
Question 3 (24 marks) Wonderful Technology Company Limited sells computers and accessories. Data of the store's operations are as follow: Sales are budgeted at $400,000 for December 2019, $420,000...
Kratz Manufacturing Company uses an activity-based costing system. It has the following manufacturing activity areas, related cost drivers and cost allocation rates: Activity Cost Driver Cost...
You are a Partner with Fix-It Consultants and have been engaged in an advisory capacity with a software company, called MoveFast. The company is seeing a sharp decline in revenue, with the primary...

Let (X) be an arbitrary set and (mathscr{F} subset mathscr{P}(X)). Show that [sigma(mathscr{F})=bigcup{sigma(mathscr{C}): mathscr{C} subset mathscr{F} text

Question:

Step by Step Answer:

Write o 6 C CF C is a countable subfamily If C C F we get o 6 CoF and so C G F Conversely it ...View the full answer

Measures Integrals And Martingales

Students also viewed these Business questions